Hydrologic Design 4501
Chapter 1: Hydrologic Water Cycle and Mass Balance
Ardeshir Ebtehaj
University of Minnesota
Table of Contents
Chapter 1: Hydrologic Water Cycle and Mass Balance
1- Introduction
2- Hydrology and Water Resources Managment
3- Global Freshwater Resources
4- Water Use in the United States
5- Global Water Cycle
5-1 Hydrologic watersheds
5-2 Driver of the global hydrologic water cycle
5-3 Earth's atmospheric circulation
6- Water Budget Analysis
1- Introduction
Spread of human population and formation of civilizations are correlated with the availability of fresh water.
The Mesopotamian civilization, widely considered as the cradle of civilization, was in the the area between the Tigris and Euphrates Rivers. Contemporary distribution of human population in the United State is not an exemption. It is easy to see that the climatology of precipitation somewhat has dictated the density of human population in the U.S. Most of the biggest cities and economies of the country are in the vicinity of lakes, rivers, and estuaries.
- Hydrology is the study of water and its transport in all of its phases (i.e., solid, liquid, vapor) across different elements of hydrosphere, which is a region between 1 km deep in the lithosphere and 15 km high in the atmosphere.
These days, hydrologic sciences are largely focused on terrestrial water cycle in continental and global scales under natural condition or anthropogenic impacts. Hydrologic and hydraulic engineering invlove the use and trasport of water through human control or intervention.
In Minnesota, the population is centered around the Twin Cities metropolitan area, which is at the confluence of the Mississippi and Minnesota rivers. Twin Cities are also located in the southeastern portion of the state that receives the most amount rainfall.
2- Hydrology and Water Resources Managment
For engineers, hydrologic knowledge is applied to the use and control of water resources on the land areas of the Earth, manily for the following purposes:
- Water resource management and supply
- Design of hydraulic structures
- Wastewater treatment
- Irrigation and drainage
- Hydropower, flood, and drought control
- Navigation and erosion
- Fisheries and wildlife protection
Water resources management is an interdisciplinary field that involves branches of biological sciences, engineering, physical science, and social sciences.
Water resource engineering largely involves hydrologic and hydraulic processes for water supply and water excess management as well as environmental restoration. Movement of water is explained through the laws of fluid mechanics. Application of fluid mechanics for civil engineers often manifest itself in explaining hydrologic and hydraulic processes.
- Hydrologic processes (e.g., precipitation, evaporation, runoff) involve movement of water across different natural reservoirs such between soil and atmosphere. The field of eco-hydrology explains the intersection of hydrologic and ecological processes such as plants.
Hydraulic processes include three types of water flows: (1) pressurized pipe flows, (2) open channel flows, and (3) ground-water flows.
3- Global Freshwater Resources
The following table reports water resorviors of the Earth. As is evident, the largest reservoir of freshwater is in glaciers (i.e., 1.74% of total water and 68.7% of global freshwater) and mainly in Antarctic and Greenland ice sheets. As reported, water and lakes and river are less than 0.3% of total freshwater on Earth.
4- Water Use in the United States
Water use from a hydrologic perspective is defined as all water flows that are results of human intervention in the hydrologic cycle. The national water use information program conducted by the United States Geological Survey (USGS) distinguishes the following water-use flows as follows:
- waterwithdrawals for off-stream purposes
- water deliveries at point of use or quantities released after use,
- consumptive use
- conveyance loss
- reclaimed wastewater
- return flow
- in-stream flow.
The relationships among the human-made flows at various points of measurement are illustrated in the left and and the an estimate of water use in the United States is shown in the right hand side in billion gallons per day [bgd].
5- Global Water Cycle
Hydrologic cycle occurs through water fluxes across different water reservoirs.
Water flux is the mass of water, per unit area, per time across the water reservoirs in the hydrosphere [
]. If we devide the flux of water by its density the unit will be [
], which is the unit of flow dischrage or the volumetirc water flux.The water fluxes can be in various phases such as vapor, liquid, and/or solid.
]. If we devide the flux of water by its density the unit will be [], which is the unit of flow dischrage or the volumetirc water flux.The water fluxes can be in various phases such as vapor, liquid, and/or solid. Depending on the net outflow discharge 
and volume of these reservoirs 
, each has a different residence time 
. Residence time of the main water reservoirs are:
and volume of these reservoirs , each has a different residence time . Residence time of the main water reservoirs are: - Oceans (~2500 yr)
- Groundwater (~8 yr)
- Lakes and rivers (~88 days)
- Soil moisture (~47 days),
- Atmosphere (~9 days).
Among these reservoirs, atmosphere shows the minimum residence time, an indication of its fast evolving dynamics. Groundwater residence time needs to be taken into consideration for sustainable developments in arid and semi-arid regions.
The National Aeronautics and Space Administration (NASA) of the United States prepared a clip (link: NASA: Earth's Water Cycle) that shows the global hydrologic water cycle and the role of Earth observaing satellites in measuring its changes.
A conceptual schematic of the hydrologic water cycle and involved processes and water fluxes is shown in the following figure.
- Precipitation: Conversion of atmospheric water to liquid or solid water that reaches the earth's surface. The typical unit is
-- volumeric flux of water per area. - Interception: Precipitation that does not reach the soil, but is intercepted by the leaves, branches of plants and canopy.
- Throughfall: Flux of intercepted precipitation water from plants' leaves and stems to the soil surface.
- Infiltration: Downward flux of water at the soil surface. The typical unit is -- volumeric flux of water per area.
- Overland flow: The portion of rain, snow or irrigation water that is more than the surface infiltration capacity and flows over land surface and enters into the channel flow.
- Interflow: Lateral flux of water in shallow depth, above the groundwater table, into the streams.
- Percolation: Downward flux of water between the soil surface and water table.
- Recharge: Downward flux of water at the water table. This is the flux that replenishes the groundwater.
- Baseflow: Lateral flow of groundwater into the stream flows blow the groundwater level.
- Evapotranspiration: Conversion of surface waters to water vapor through combination of direct evaporation from the soil/water surfaces and transpiration due to the vegetation metabolism. The typical unit is
-- volumeric flux of water per area. - Condensation: Conversion of water vapor to liquid water.
- Sublimation: Direct phase change from ice to water vapor. Direct phase change of water vapor to ice is called deposition.
5-1 Hydrologic watersheds
All of the above processes can be quantified over a hydrologic unit called watershed.
- A watershed is defined as a locus of all points on the earth's surface that drain precipitation water to a single point, called the watershed outlet. The boundary of a watershed is called the divide.
Watersheds can be delineated either manually or automatically using digital elevation models (DEM) and computational algorithms. The size of a watershed can range from a few acres to millions of square miles (Mississippi River basin, 3.2 million square miles) -- depending on the geomorphologic characteristics of land surfaces and location of the outlet. Watersheds have a nested structure.
5-2 Driver of the global hydrologic water cycle
Solar radiative energy from the Sun is the main driver of the global water cycle. Although the earth is a closed thermodynamic system (no mass exchange with its environment), it is not an isolated system as it exchanges energy with the outer space. This exchange is a consequence of the annual average solar radiation flux of 342 
, over the entire Earth surfaces, at the top of its atmosphere.
, over the entire Earth surfaces, at the top of its atmosphere. Due to the ellipsoidal shape and orbital geometry of earth, the equators receive more energy than polar regions. This differential energy budget eventually leads to a pressure gradient in the air atmosphere from equators to poles that circulates the Earth's atmosphere. The moving air masses transport water vapor from tropical oceans and precipitate them over lands. The precipitation water returns back to the atmosphere and oceans through the explained fluxes and processes such as evapotranspiration, infiltration, percolation, runoff, and streamflow.
5-3 Earth's atmospheric circulation
As explained, the convective motion of air and water masses in atmosphere are mainly because of an existing pressure gradient. Why does such a pressure gradient exist?
As a general rule, when the temperature of an air parcel increases at a constant pressure, based on the ideal gas law, its density reduces and vice versa.
Therefore, in general, a cold air mass is denser than a warm air mass at constant pressure. Because the air is compressible, the density of cold air column decays faster than the density of a warm air column from earth surface to higher altitudes. Due to higher pressure of warm air column aloft than the cold air column, the air flows from warm to cold regions at high elevations.
As the air flows from warm to cold areas, the cold air column becomes heavier and its pressure increases at the surface. As a result, a surface air flow forms from cold to warm areas which eventually gives rise to a circulation pattern.
The circulation of the earth's atmosphere is due to formation of a pressure gradient from warm (tropics) to cold (polar regions) air masses.
According to the above simple conceptualization of the atmospheric circulation, one may think of the Earth atmospheric circulation as shown in the figure below. However, the one-cell circulation model does not exist because these large eddies are unstable and more importantly there are other forces acting on the traveling air parcels that break these large hypothetical circulation cells apart. One of the main forces is the called the Coriolis force.
In simple terms, with respect to the a rotating reference frame, it appears that the Coriolis force is deflecting an object that moves from the center to the perimeter and vice versa.
Coriolis force deflects an object thrown from point A to point B to the right of its path in a counter clockwise rotational system. This force is due to a combined effect of the angular (
) and linear velocity (
).
) and linear velocity (). 
The Coriolis force deflects air parcels to the right and left of the their moving direction in the Northern and Southern Hemisphere, respectively, as shown in the above figure.
As a result of the coriolis and pressure gradient forces, those large hypothetical circulation cells breaks into three smaller cells as shown below. It is easy to conclude that the surface air flows from mid-latitudes high-pressure divergence zones towards the tropical low-pressure convergence zones are deflected towards east. These surface air flows are called Easterlies or trade winds. On the other hand, surface air flows from high-pressure horse latitudes towards polar fronts are deflected to the west and create the Westerlies.
The coriolis force has another important implications in formation and direction of tropical and extra tropical storms. In regions within ±5-20 latitudes, the coriolis force is strong enough to create cyclonic activities around the high and low pressure areas. Based on the explained coriolis effect, it is easy to understand that the air flows counter clockwise around lows and clockwise around highs in the Northern Hemisphere.
A schematic of airflow in a low pressure cell (left) with convergence at the surface and divergence aloft. Airflows in a high pressure cell diverges at the surface and converges aloft. A satellite footage of the Hurricane Irma shows its counter clock-wise rotation around a strong low-pressure system.
6- Water Budget Analysis
Water budget analysis is extremely important for sustainability of socioeconomic growth.
Formerly, one of the four largest lakes in the world with an area of 68,000 sq-km (26,300 sq-mi), the Aral Sea has been steadily shrinking since the 1960s after the rivers that fed it were diverted by Soviet irrigation projects. By 1997, it had declined to 10% of its original size.
The right hand side shows Iran’s Lake Urmia, which was one of the largest saltwater lakes in the world. With eight times as much salt as seawater, it was the globe’s largest habitat for brine shrimps, which attract flamingos, other birds as they migrate across Asia. But the lake is shirinking. Using images captured by USGS-NASA Landsat satellites, it is determined that its area has decreased by 88% since the 1970s. Many blamed severe drought, but climate data from satellites and other sources demonstrated that the lake is shrinking even in wet years. Therefore, research suggests that the reason is unsustainable agricultural developments. As water retreats, it leaves behind a salty crust that is swept into the air by dust storms. These particles can cause respiratory problems in humans and on nearby agricultural lands. The bottom panel shows that the Great Salt Lake in Utah, United States, is also shrinking.
